Question

Calculati valoarea sumei s=3+E(2)+E(3)+E(4)+...+E(100).
E(x)=6 supra x(x+1).

Answer 1

E(2)=6 /2(2+1)= 6/2*3= 2/2=1
E(3)=6/ 3(3+1)= 6/ 3*4= 2/4=1/2
E(4)=6 /4 (4+1)= 6/4*5= 3/2*5= 3/10
..............................................
E(100)=6/ 100(100+1)= 6/100*101= 3/50 *101= 3/5050

S=3 +(1+ 3/5050)/2 *100  aducem la acelasi numitor in paranteza
=3+ (5050+1)/5050 *50
=3+ 5051*101
=3+ 510 151
=510 154